In this article, we shall study the approximate controllability of certain non-autonomous second-order nonlinear differential problems with finite delay in the infinite dimensional space. Sufficient conditions are proposed and proved for the controllability of such systems. Further, we briefly discuss the approximate controllability of impulsive as well as integro-differential problem. We establish these results by utilizing Schauder’s fixed-point analysis approach. Finally, the application of the proposed results is presented by giving an example.

中文翻译：

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具有时滞的二阶非自治系统的近似可控性

在本文中，我们将研究在无限维空间中具有有限时滞的某些非自治二阶非线性微分问题的近似可控性。提出并证明了这种系统的可控性的充分条件。此外，我们简要讨论了脉冲以及积分微分问题的近似可控性。我们利用Schauder的定点分析方法建立了这些结果。最后，通过举例说明提出的结果的应用。